On a recent Thursday, in an operating theater at the Wild Animal Sanctuary in Keenesburg, Colorado, a mountain lion named Montana lay on his side, unconscious. Two veterinary dentists stood at his head, scraping infected pulp out of his four canine teeth, all of which needed root canals. Occasionally, one of the dentists raised an X-ray machine to the lion’s head to check his progress. While they worked, a veterinarian a few feet away removed Montana’s testicles, a bloody procedure. When she finished, she packed them up for transport to a lab, where she planned to use them to grow stem cells.

In the next room, a caged black leopard named Backara, his spots visible from up close, waited to undergo the same set of procedures. A technician put the hundred-and-forty-pound animal to sleep with an injection, then four people maneuvered him onto a cloth stretcher and carried him into the operating room. They set him down almost perpendicular to Montana, on a grate attached to a pulley system for large animals, before getting to work. (When the sanctuary’s grizzly bears, which can weigh more than fifteen hundred pounds, need work, they are anaesthetized in their habitat and brought to the operating room by forklift and truck.)

As the procedures went on, Peter Emily, a vigorous eighty-two-year-old who helped to pioneer the field of wild-animal dentistry, darted around the room in a surgical scrub shirt. Emily, who is semi-retired, consulted with the other dentists, inspected both of the anaesthetized animals’ mouths, and chatted with guests, speaking quickly, in a raspy voice. He soon took a more hands-on role with Backara, who had a molar that required extraction.

Recently, a San Francisco-based start-up called Big Health launched an iOS app, Sleepio, that features an animated psychotherapist named the Prof. The avuncular, grey-templed Scotsman guides users through a course, based on the principles of cognitive-behavioral therapy (C.B.T.), that is designed to treat insomnia. C.B.T’s basic principles are simple enough that patients can follow them with a book, but the company hopes to capture some of the dynamics of in-person therapy, which means encouraging its users to bond emotionally with its digital shrink­.

When the Prof first appears, he’s waving hello in silhouette against the sun. He has a stocky body and skinny legs—proportions that suit an iPhone screen—and he’s dressed in a natty red sports jacket and a black tie. Users eventually learn that he rides in a hot-air balloon and that he has a narcoleptic hound named Pavlov. His gestures—for example, swinging his arms and grabbing his lapels—project an appealing vigor. Like a sportscaster, the Prof is frequently offscreen, so his voice is probably the most crucial aspect of the experience.

Big Health tested regional British accents before settling on an optimistic but gentle brogue. “It combined authority with approachability, but yet with a sort of a no-nonsense streak that can nudge you towards doing a bit better,” the company’s C.E.O., Peter Hames, told me. The role ultimately went to a voice actor who lives in Glasgow. Hames added that the company is open to creating a figure with a more familiar voice—perhaps a woman. Though he says that the app is equally effective in treating insomnia in both men and women, anecdotal evidence suggests that the sexes don’t respond to the Prof in the same way. Men tend to absorb lessons without noticing him, while women are more inclined to form a bond. According to Hames, one woman reported, “When he congratulates me I feel great.”